1,331 research outputs found
On Generalizations of Network Design Problems with Degree Bounds
Iterative rounding and relaxation have arguably become the method of choice
in dealing with unconstrained and constrained network design problems. In this
paper we extend the scope of the iterative relaxation method in two directions:
(1) by handling more complex degree constraints in the minimum spanning tree
problem (namely, laminar crossing spanning tree), and (2) by incorporating
`degree bounds' in other combinatorial optimization problems such as matroid
intersection and lattice polyhedra. We give new or improved approximation
algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure
Structural relaxation around substitutional Cr3+ in MgAl2O4
The structural environment of substitutional Cr3+ ion in MgAl2O4 spinel has
been investigated by Cr K-edge Extended X-ray Absorption Fine Structure (EXAFS)
and X-ray Absorption Near Edge Structure (XANES) spectroscopies.
First-principles computations of the structural relaxation and of the XANES
spectrum have been performed, with a good agreement to the experiment. The Cr-O
distance is close to that in MgCr2O4, indicating a full relaxation of the first
neighbors, and the second shell of Al atoms relaxes partially. These
observations demonstrate that Vegard's law is not obeyed in the MgAl2O4-MgCr2O4
solid solution. Despite some angular site distortion, the local D3d symmetry of
the B-site of the spinel structure is retained during the substitution of Cr
for Al. Here, we show that the relaxation is accomodated by strain-induced bond
buckling, with angular tilts of the Mg-centred tetrahedra around the Cr-centred
octahedron. By contrast, there is no significant alteration of the angles
between the edge-sharing octahedra, which build chains aligned along the three
four-fold axes of the cubic structure.Comment: 7 pages, 4 figure
Part 1: a process view of nature. Multifunctional integration and the role of the construction agent
This is the first of two linked articles which draw s on emerging understanding in the field of biology and seeks to communicate it to those of construction, engineering and design. Its insight is that nature 'works' at the process level, where neither function nor form are distinctions, and materialisation is both the act of negotiating limited resource and encoding matter as 'memory', to sustain and integrate processes through time. It explores how biological agents derive work by creating 'interfaces' between adjacent locations as membranes, through feedback. Through the tension between simultaneous aggregation and disaggregation of matter by agents with opposing objectives, many functions are integrated into an interface as it unfolds. Significantly, biological agents induce flow and counterflow conditions within biological interfaces, by inducing phase transition responses in the matte r or energy passing through them, driving steep gradients from weak potentials (i.e. shorter distances and larger surfaces). As with biological agents, computing, programming and, increasingly digital sensor and effector technologies share the same 'agency' and are thus convergent
Tailoring Glass Properties: Why Chemical Composition and Thermal Treatments Matter
Architectural use of glass dates back from the beginning of our era when it wasused to make windows. Its range of chemical composition was close to that ofcurrent flat or hollow glass, illustrating early optimization of both productionprocess and material properties. In modern buildings glass is ubiquitous, highlyvisible as in facades or hidden as fibers for thermal insulation or for high-speedtelecommunication. This short review describes the main factors that have madethis variety of uses possible. The fundamental point is the amorphous nature ofglass, which allows pieces of any shape and size to be produced and the propertiesof the material to be tailored through thermal treatments and incorporation of a hostof chemical elements in widely different proportions
Plato's cube and the natural geometry of fragmentation
Plato envisioned Earth's building blocks as cubes, a shape rarely found in
nature. The solar system is littered, however, with distorted polyhedra --
shards of rock and ice produced by ubiquitous fragmentation. We apply the
theory of convex mosaics to show that the average geometry of natural 2D
fragments, from mud cracks to Earth's tectonic plates, has two attractors:
"Platonic" quadrangles and "Voronoi" hexagons. In 3D the Platonic attractor is
dominant: remarkably, the average shape of natural rock fragments is cuboid.
When viewed through the lens of convex mosaics, natural fragments are indeed
geometric shadows of Plato's forms. Simulations show that generic binary
breakup drives all mosaics toward the Platonic attractor, explaining the
ubiquity of cuboid averages. Deviations from binary fracture produce more
exotic patterns that are genetically linked to the formative stress field. We
compute the universal pattern generator establishing this link, for 2D and 3D
fragmentation.Comment: main: 6 pages, 6 figures, supplementary: 18 pages, 12 figure
Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
We investigate the zero temperature structure of a crystalline monolayer
constrained to lie on a two-dimensional Riemannian manifold with variable
Gaussian curvature and boundary. A full analytical treatment is presented for
the case of a paraboloid of revolution. Using the geometrical theory of
topological defects in a continuum elastic background we find that the presence
of a variable Gaussian curvature, combined with the additional constraint of a
boundary, gives rise to a rich variety of phenomena beyond that known for
spherical crystals. We also provide a numerical analysis of a system of
classical particles interacting via a Coulomb potential on the surface of a
paraboloid.Comment: 12 pages, 8 figure
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